The operators on the set valued function spaces and some applications

In the first chapter of this study entitled "The Operators on the Set Valued Function Spaces and Some Applications " a summary of the literature related to the interval analysis is given. Further, the application areas of this study are presented. In the second chapter, some fundametal definitions and theorems used in the next chapter are given. Morever, the spaces L^{p}(R),1≤p<∞ and some important properties of these spaces ara analyzed. Next, the basic concept of the signal processing are presented. In the third chapter, the measurability, continuity and Aumann integral of the set-valued functions are mentioned. In the fourth chapter, quasilinear spaces, quasilinear operators and quasilinear inner product spaces are introduced. Also, some basic results related to these spaces are given. In the fifth chapter, first the notion of interval signal is introduced and the definition of a complex interval is given. Then, it is shown that the space of the complex intervals has the quasilinear space structure. Further, the characteristical properties of this space are examined. Last, an application with respect to the notion of interval signal is given. In the sixth chapter, the spaces L^{p}(R,Ω(C)),1≤p<∞ that are defined from the set of real numbers to the space of all compact-convex subsets of complex numbers for which the pth power of their norm is integrable are investigated. Further, an inner-product on L²(R,Ω(C)) is defined by the aid of Aumann integral and it is shown that L²(R,Ω(C)) is a Hilbert quasilinear space. Next, translation, modulation and dilation operators on the space L²(R,Ω(C)) are given. In the seventh and last chapter, primarily Fourier transform on the space L¹(R,Ω(C)) is described. After the notion of the Fourier transform is expanded to the space L²(R,Ω(C)). Finally, an application regarding the Fourier transform of an interval signal is given.